Estimating population percentages on a normal curve

Estimating population percentages on a normal curve

-bell curved

- symmetric about the mean

- the total area under the curve is 1

Normal Distribution Graph

Lesson Problem

In a school, the weights of students are normally distributed with mean 61kg and standard deviation 8 kg. What percentage of students between 50.6kg and 61.64kg?

As you sketch the bell curve add in all known information.

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​Sketch the bell curve

Take the information and enter it into a probability statement.

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​Probability Statement

You normalize the data by subtracting the mean from the data and dividing by the standard deviation. Input your data into the probability equation.

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​Normalize the Data

As you simplify the equation you find the probability for Z.

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Simplify the equation

Using your data, sketch the graph. We can see the data centered around zero and classify it with two regions.

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​Sketch the graph

We can see how the region on the right is in the correct format for us to look up with tables.

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Correct Format

Use this data to find values in the Standard Normal Distribution Tables.

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​Standard Normal Distribution Tables

Add the values together and find the percentage.

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Calculate the percentage

Fill in the Blank

The number of eggs laid per year laid by a particular breed of chicken is normally distributed with a mean of 225 and a standard deviation of 10 eggs. About what percent of the chickens will lay between 215 and 235 eggs per year?

%

Lesson Summary

Steps to estimate a population percentage:

• Sketch the bell curve

• Make a probability statement

• Normalize the data

• Simplify the equation

• Sketch graph

• Use standard normal distribution tables

• Calculate the percentage

I used nagwa.com for visual components.